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A device-independent dimension test for a Bell experiment aims to estimate
the underlying Hilbert space dimension that is required to produce given
measurement statistical data without any other assumptions concerning the
quantum apparatus. Previous work mostly deals with the two-party version of
this problem. In this paper, we propose a very general and robust approach to
test the dimension of any subsystem in a multiparty Bell experiment. Our
dimension test stems from the study of a new multiparty scenario which we call
prepare-and-distribute. This is like the prepare-and-measure scenario, but the
quantum state is sent to multiple, non-communicating parties. Through specific
examples, we show that our test results can be tight. Furthermore, we compare
the performance of our test to results based on known bipartite tests, and
witness remarkable advantage, which indicates that our test is of a true
multiparty nature. We conclude by pointing out that with some partial
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